Gini and concentration indexes are well known useful tools in analysing redistribution and re-ranking effects of taxes with respect to a population of income earners. Aronson, Johnson and Lambert (1994), Urban and Lambert (2008) decompose Gini and re-ranking indices to analyse potential redistribution effects and the unfairness of a tax systems. Urban and Lambert (2008) consider contiguous income groups which are created by dividing the pre-tax income parade according to the same bandwidth. However, earners may be very often split into groups characterized by social and demographic aspects or by other characteristics: in these circumstances groups can easily overlap. In this paper we consider a more general situation that takes into account overlapping among groups; we obtain matrix compact forms for Gini and concentration indexes, and consequently, for redistribution and re-ranking indexes. In deriving formulae the so called matrix Hadamard product is extensively used. Matrix algebra allows to write indexes aligning incomes in a non decreasing order either with respect to post-tax income or to pre-tax incomes. Moreover, matrix compact formulae allow an original discussion for the signs of the within group, across group, between and transvariation components into which the Atkinson-Plotnick-Kakwany (Plotnick, 1981) re-ranking index can split.
|Titolo:||Playing with the Hadamard product in decomposing Gini, concentration, redistribution and re-ranking indexes|
VERNIZZI, ACHILLE (Primo)
|Data di pubblicazione:||31-lug-2009|
|Parole Chiave:||Gini and concentration indexes decompositions ; Tax redistributive effects ; Tax re-ranking effects ; Hadamard product|
|Settore Scientifico Disciplinare:||Settore SECS-P/05 - Econometria|
|Citazione:||Playing with the Hadamard product in decomposing Gini, concentration, redistribution and re-ranking indexes / A. Vernizzi. - Milano : Department of Economics in Milano university, 2009 Jul 31.|
|Appare nelle tipologie:||08 - Relazione interna o rapporto di ricerca|